The technique of spectrometry is used widely to determine spectra either occurring in nature or in laboratory settings. Recent advances have provided significant improvements in spectrometric applications such as astronomical spectrometry. Prior to 1980, measurements of Doppler velocity shifts providing velocity precisions on the order of 1 km s−1 were seldom possible. Now, using high precision absorption-cell spectrometers, measurement of velocities with precisions as small as 1 m s−1 are attainted. These data make possible the detection of planetary companions to stars on the order of 0.16MJ<M sin(i)<15MJ (MJ is the mass of Jupiter, and i is the inclination angle of the orbit of the planetary companion). It would be desirable, however, to obtain a greater sensitivity capability to detect smaller companions or to provide greater sensitivity in other types of non-astronomical applications.
Another available technique is Fourier Transform Spectrometry (FTS). An FTS spectrometer is an autocorrelation, or time-domain, interferometer. The theoretical basis was laid at the end of the 19th century (Michelson, A. A. 1891, Phil. Mag., 31, 256, Michelson, A. A. 1892, Phil. Mag., 34, 280.), but FTSs did not achieve widespread use until approximately 75 years later (Brault, J. W. 1985, in High Resolution in Astronomy, 15th Advanced Course of the Swiss Society of Astrophysics and Astronomy, eds. A. Benz, M. Huber and M. Mayor, [Geneva Observatory: Sauverny], p. 3.).
Fellgett described the first numerically transformed two-beam interferogram and applied the multiplex method to stellar spectroscopy (Fellgett, P., J. de Physique et le Radium V. 19, 187, 236, 1958). Fellgett employed a Michelson-type interferometer 10 as shown in FIG. 1, wherein the incoming beam of light B is divided into two beams B1 and B2 by a beamsplitter (“beam divider”) 12. B1 is reflected from retro reflector 14, while B2 is reflected from retroreflector 16. As shown, beams B1 and B2 follow separate paths whose lengths can be precisely adjusted by delay lines (DLs) established by repositioning one or both of reflectors 14 and 16, as shown with reflector 16 connected to drive train 18 and drive motor 20. The beams, now with a path difference x (i.e. the “lags”), are recombined at beamsplitter 12 and focused by a concave mirror 22 onto a detector 24, producing an interferogram I(x), where
                                                        I              d                        ⁡                          (                              x                i                            )                                =                                    ∫                              s                min                                            s                max                                      ⁢                                                  ⁢                                          ⅆ                s                            ⁢                                                          ⁢                                                J                  t                                ⁡                                  (                  s                  )                                            ⁢                              cos                ⁡                                  (                                      2                    ⁢                                                                                  ⁢                    π                    ⁢                                                                                  ⁢                                          x                      i                                        ⁢                    s                                    )                                                                    ,                                      (          1          )                ,            as is discussed in more detail below. A mirror 28 is provided for an optional reference beam indicated in FIG. 1 by the dotted lines. The reference beam is divided into two beams at the beamsplitter 12. These two beams are reflected from the retroreflectors 14 and 16, are recombined at 12 and focused by 22 onto the detector 24. The reference beam allows the user to align the optics as well as to determine the zero-path position of the DLs, i.e., the position of retroreflectors 14 and 16 for which the path difference x=0. In this manner, the reference beam thereby measures the delay, that is, the path difference x, introduced by the delay lines. This provides a more accurate determination of the optical path differences in the interferometer, and is typically included in applications involving the precise determination of spectral lineshapes and Doppler shifts. The detector is output to an amplifier and demodulator 30, and then the interferogram corresponding to the input spectrum is output to a recorder 32.
The intensity of the combined beam is measured for a series of delay line positions. The wavelengths in the light beam cover a range from λmin to λmax, i.e., centered on λ0 and covering a range Δλ=λmax−λmin. The most important length parameter in the FTS is the lag, x, which is equal to the path length difference A−B. At any given wavelength λ, complete constructive interference between light from the two paths occurs when x/λ is an integer, and complete destructive interference occurs when x/λ is an integer plus ½.
When the paths A and B are precisely equal to within a small fraction of λ0 (i.e., x=0 is the only delay for which x/λ=0 at all wavelengths), the light waves at all wavelengths in the two beams constructively interfere and the intensity I in the recombined beam is at its maximum, Imax. This position is known as the central fringe. As the DLs are moved and x changes, constructive interference between light waves from the two paths weakens, particularly at the shorter wavelengths, and I decreases. As the magnitude of x continues to increase, I reaches a minimum at x/λ0=½ and then rises again to a new (but weaker) maximum at x/λ0=1. This weakening oscillation of I continues as x increases. When x/λ0 is increased to many times λ0/Δλ, some wavelengths interfere constructively and some destructively, so I is close to the mean light level. Thus, if the observed spectral region is wide, there is only a small range of lag with large deviations from the mean level.
The resulting data set of intensity measurements, I(x), measured at many values of x is known as an interferogram (Equation 1) as discussed above. The region of x over which there are large deviations from the mean level is termed the fringe packet. An example of a typical interferogram is shown in FIG. 2. The wavelength of the high frequency oscillations is the central wavelength of the bandpass, λ. As shown, the number of fringes in the central fringe packet is approximately equal to λ/Δλ, where Δλ is the bandwidth.
Typically, the interferogram is sampled in steps of λ0/2, and is then Fourier transformed to produce a spectrum. The spectrum is given as a series of values at regularly spaced discrete values of the wavelength, λ. The spectrum that results from the Fourier transform of the interferogram contains artifacts of the PSF, which results from the finite lag range and the actual sampling of the interferometer. A wide range of deconvolution methods have been developed to disentangle the real signal from the deleterious effects of sampling, noise, etc., and have generally done so by implicitly modeling the spectrum as differing from zero only at discrete values of wavelength. The disadvantage of the deconvolution approaches is that they are highly nonlinear processes, so their behavior and uncertainties are hard to understand quantitatively. In addition, the disadvantage of modeling the spectrum only at discrete points is that the corresponding interferogram has significant sidelobes.
The resolution of the spectrum at a given wavelength, λ, is determined by the maximum value of x/λ and can be understood as follows. The light waves that comprise a narrow spectral line occupy only a small range of wavelengths, and thus stay correlated for a relatively long time, given roughly by δλ/c, where δλ is the range of wavelengths making up the line and c is the speed of light. Since the lag x corresponds to a time delay between beams of x/c, a narrow line produces interference fringes over a large range of x. The FTS can measure over only a finite range in x, so it cannot distinguish between a spectral line of width δλ and a narrower line that produces fringes over a larger range of x. For a spectral line wider than the resolution of the FTS, the width of a spectral feature is measured by the range of x over which there are interference fringes.
The most common type of spectrometer is a dispersing spectrometer, consisting of a dispersing element (usually a grating) and a camera equipped with an array of detectors (usually a CCD) for multiplexing the dispersed output. Present CCD designs allow the number of channels Nch to exceed several thousand, so that the entire integration time is directed to integrating on all Nch channels. Recent planetary detections have used dispersing spectrometers with an absorption cell positioned in the path of the incoming beam to impose a reference set of spectral lines of known wavelength on the stellar spectrum.
In principle, an FTS offers at least three major advantages over a dispersing spectrometer. First, the spectral resolution can be changed simply by changing the maximum value of the lag; second, the wavelength scale in the resulting spectrum is determined only by the delay line settings, while remaining insensitive to such effects as scattered light and flexure of the instrument; and third, the point spread function (PSF) of the spectrum can be determined to a high degree of precision.
An FTS, however, also suffers certain disadvantages. These include low sensitivity: a conventional FTS is essentially a single-pixel scanning interferometer, and high spectral resolution requires measurements at a large number of lag settings. Accordingly, FTSs are commonly used when sensitivity is not a paramount concern, such as with laboratory spectroscopy or solar observations, or when very high spectral resolution or accurate wavelength calibration is required, such as in observations of planetary atmospheres. Other applications of FTSs include FTIR, MRI, and fluorescence and Raman emission spectroscopy.
It would therefore be desirable to provide a spectrometer which offers the advantages of an FTS spectrometer while preserving most of the sensitivity of a dispersing spectrometer. It would also be desirable to provide an improved algorithm for recovering the spectrum from the interferogram with greater fidelity, with easily quantifiable error estimates, and without producing undesirable artifacts.